Galois Theory: Recap and Transitivity

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Ramification and Structure of Finite Extensions

Explores ramification and structure of finite extensions of Qp, including unramified extensions and Galois properties.

Topology: Homomorphisms and Galois Theory

Explores homomorphisms in topology and delves into Galois theory.

Galois Theory Fundamentals

Explores Galois theory fundamentals, including separable elements, decomposition fields, and Galois groups, emphasizing the importance of finite degree extensions and the structure of Galois extensions.

Finite Degree Extensions

Covers the concept of finite degree extensions in Galois theory, focusing on separable extensions.

Galois Theory: The Galois Correspondence

Explores the Galois correspondence and solvability by radicals in polynomial equations.

Galois Theory: Extensions and Residual Fields

Explores Galois theory, unramified primes, roots of polynomials, and finite residual extensions.

Classification of Extensions

Explores the classification of extensions in group theory, emphasizing split extensions and semi-direct products.

Galois Theory of Qp

Explores the Galois theory of Qp, covering algebraic extensions, inertia groups, and cyclic properties.

Decomposition & Inertia: Group Actions and Galois Theory

Explores decomposition groups, inertia subgroups, Galois theory, unramified primes, and cyclotomic fields in group actions and field extensions.

Galois Theory: Solvability and Radical Extensions

Explores solvability by radicals in Galois theory and the Galois/Abel criterion for solvability.